Neural modeling fields

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Neural modeling field (NMF) theory mathematically implements the mind mechanisms including concepts, emotions, instincts, imagination, thinking, understanding, language, interaction between language and cognition, the knowledge instinct, conscious, unconscious, aesthetic emotions including beautiful and sublime. NMF provides a foundation for modeling evolution of languages, consciousness, and cultures.

NMF is a multi-level, hetero-hierarchical system [1]. The mind is not a strict hierarchy; there are multiple feedback connections among adjacent levels, hence the term hetero-hierarchy. At each level in NMF there are concept-models encapsulating the mind’s knowledge; they generate so-called top-down signals, interacting with input, bottom-up signals. These interactions are governed by the knowledge instinct, which drives concept-model learning, adaptation, and formation of new concept-models for better correspondence to the input, bottom-up signals.

Here we describe a basic mechanism of interaction between two adjacent hierarchical levels of bottom-up and top-down signals (fields of neural activation; in this aspect NMF follows[2]; sometimes, it will be more convenient to talk about these two signal-levels as an input to and output from a (single) processing-level. At each level, output signals are concepts recognized in (or formed from) input, bottom-up signals. Input signals are associated with (or recognized, or grouped into) concepts according to the models and the knowledge instinct at this level. This general structure of NMF corresponds to our knowledge of neural structures in the brain; still, here we do not map mathematical mechanisms in all their details to specific neurons or synaptic connections. The knowledge instinct is described mathematically as maximization of a similarity measure. In the process of learning and understanding input, bottom-up signals, concept-models are adapted for better representation of the input signals so that similarity between the concept-models and signals increases. This increase in similarity satisfies the knowledge instinct and is felt as aesthetic emotions.


At a particular hierarchical level, we enumerate neurons by index n=1,2..N. These neurons receive input, bottom-up signals, X(n), from lower levels in the processing hierarchy. X(n) is a field of bottom-up neuronal synaptic activations, coming from neurons at a lower level. Each neuron has a number of synapses; for generality, we describe each neuron activation as a set of numbers, X(n) = {Xd(n), d = 1,... D}. Top-down, or priming signals to these neurons are sent by concept-models, Mm(Sm,n); we enumerate concept-models by index m=1,2..M. Each model is characterized by its parameters, Sm; in the neuron structure of the brain they are encoded by strength of synaptic connections, mathematically, we describe them as a set of numbers, Sm = {Sma, a = 1,... A}.

Models represent signals in the following way. Say, signal X(n), is coming from sensory neurons activated by object m, characterized by parameters Sm. These parameters may include position, orientation, or lighting of an object m. Model Mm(Sm,n) predicts a value X(n) of a signal at neuron n. For example, during visual perception, a neuron n in the visual cortex receives a signal X(n) from retina and a priming signal Mm(Sm,n) from an object-concept-model m. Neuron n is activated if both the bottom-up signal from lower-level-input and the top-down priming signal are strong. Various models compete for evidence in the bottom-up signals, while adapting their parameters for better match as described below. This is a simplified description of perception. The most benign everyday visual perception uses many levels from retina to object perception. The NMF premise is that the same laws describe the basic interaction dynamics at each level. Perception of minute features, or everyday objects, or cognition of complex abstract concepts is due to the same mechanism described below. Perception and cognition involve concept-models and learning. In perception, concept-models correspond to objects; in cognition models correspond to relationships and situations.


Learning is an essential part of perception and cognition, and it is driven by the knowledge instinct. It increases a similarity measure between the sets of models and signals, L({X},{M}). The similarity measure is a function of model parameters and associations between the input bottom-up signals and top-down, concept-model signals. For concreteness the following text refers to an object perception using simplified terminology, as if perception of objects in retinal signals occurs in a single level.

In constructing a mathematical description of the similarity measure, it is important to acknowledge two principles (which are almost obvious). First, the visual field content is unknown before perception occurred and second, it may contain any of a number of objects. Important information could be contained in any bottom-up signal; therefore, the similarity measure is constructed so that it accounts for all bottom-up signals, X(n),


L({X},{M}) = ∏n=1..N l(X(n)).


References

  1. ^ [1]: Perlovsky, L.I. 2001. Neural Networks and Intellect: using model based concepts. New York: Oxford University Press
  2. ^ Perlovsky, L.I. (2006). Toward Physics of the Mind: Concepts, Emotions, Consciousness, and Symbols. Phys. Life Rev. 3(1), pp.22-55.

Leonid Perlovsky